Straighten non planar vertices into a circle
Yes, for straightening that circle you can do like @Duarte Farrajota Ramos said (selecting that circle and pressing S+Z+0)

But that topology will sooner or later cause issues, so I did a quick gif to show you an example of fixing that topology, it stretched a few lines but nothing too noticeable on the mesh.



What I did:


I straightened that circle with
S+Z+0) 
Since this object can be perfectly mirrored on all sides I deleted
the left and back part to modify it faster.
Then I started to merge some vertices using W>Merge>At Last
I duplicated that part and inverted with S(lock on an Axis)>-1
And then I joined all parts using the Snapping Tool to Merge at the Closest Vertex.
Finaly I Removed Doubles with W>Remove Doubles